Note : Use any software package for solving the problems ( Excel, SPSS, Minitab....)
1. An investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain ( or loss, if negative) over the year. The investor believes there are five possible scenarios for the national economy in the coming year- rapid expansions, moderate expansions, no growth, moderate contractions and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively 23%, 18%,15%,9% and 3% .Also she has assessed the probabilities of these outcomes are 0.12, 0.40,0.25, 0.15 and 0.08. Use this information to describe the probability distribution of the market return. Calculate, average return, standard deviation and variance of the probability distribution of the market return for the coming year and comment.
2. The personnel department of ZTel, a large communication company, is reconsidering its hiring policy. Each applicant for a job must take a standard exam and to hire or no hire decision depends at least in part on the result of the exam. The scores of all applicants have been examined closely. They are approximately normally distributed with mean 525 and standard deviation 55.
The current hiring policy occurs in two phase. The first phase separates all applicants into three categories: automatic accepts, automatic rejects and maybe. The automatic accepts are those whose test scores are 600 or above. The automatic rejects are those whose test scores are 425 and below. All other applicants ( the maybes) are passed on to the second phase where their previous job experience, special talents, and other factors are used as hiring criteria. The personnel manager at ZTel wants to calculate the percentage of applicants who are automatic accepts or rejects, given the current standards. She also wants to know how to change the standards to automatically reject 10% of all applicants and automatically accept 15% of all applicants.
3. The following table shows the amount spent on advertising and the corresponding sales of the product from 10 companies
|
Company
|
Sales £ ('000)
|
Advertising cost £ ('000)
|
|
A
|
25
|
8
|
|
B
|
35
|
12
|
|
C
|
29
|
11
|
|
D
|
24
|
5
|
|
E
|
38
|
14
|
|
F
|
12
|
3
|
|
G
|
18
|
6
|
|
H
|
27
|
8
|
|
I
|
17
|
4
|
|
J
|
30
|
9
|
(a) Plot a scatter diagram showing the relationship between advertising cost and sales of the product.
(b) Identify the dependent and independent variables
(c) Calculate the equation of the regression line of sales on advertising costs.
(d) Use the regression line to forecast sales if advertising costs were £1000.
(e) Determine coefficient of determination and interpret